Help please! I think this is the way to solve this problem, but am not sure. Any help is most appreciated. Thanks!
Simplify
(p^4 + m p^2m)^-4/(p^-4)^-m
I see this as
1/[(p4 + mp2m)4(p4)
anything else done, such as expanding that binomial, would not considered "simplifying"
You said you think there is a way to 'solve' this,
what exactly were you thinking?
either adding or multiplying exponents
The possible answers are as follows
p^-16m + 16
p^-8m – 4
p^-11m – 4
p^-3m + 16
To simplify this expression, let's start by expanding and simplifying the numerator and denominator separately.
Numerator: (p^4 + m p^2m)^-4
To simplify this, we need to apply the rules of exponents. We know that when we raise a sum to a power, we distribute the power to each term inside the parentheses. So, in this case, we distribute the -4 exponent to each term inside the parentheses:
(p^4 + m p^2m)^-4 = p^-16 + (m p^2m)^-4
Now let's simplify the second term:
(m p^2m)^-4 = (m^1 p^2m)^-4
Using the rule that (a^m)^n = a^(m*n):
(m^1 p^2m)^-4 = m^(-4*1) p^(2*1*1) = m^-4 p^2
So, the numerator becomes:
(p^4 + m p^2m)^-4 = p^-16 + m^-4 p^2
Denominator: (p^-4)^-m
To simplify the denominator, we need to apply the rule of negative exponents. When we have a negative exponent, we can rewrite the expression by flipping the base to become positive and changing the exponent's sign. Therefore, (p^-4)^-m becomes (p^4)^m:
(p^-4)^-m = (p^4)^m = p^(4*m) = p^4m
Now we can simplify the whole expression:
(p^4 + m p^2m)^-4/(p^-4)^-m = (p^-16 + m^-4 p^2)/(p^4m)
Now, we have a simplified expression.